Is it safe to use a 11.1V 1300mAh LiPo Battery designed for RC cars/planes with my new Arduino Nano? I read that the Nano can operate on 6-20V with 7-12V being recommended, so it sounds to me like it would be fine?

Also, I know I plug the positive lead into VIN (pin 30) so do I plug the negative lead into GND?

It's been a while since I've done any electronics tinkering, please excuse my noobiness.

Yes that should be fine. If you are using the Nano to supply lots of current its regulator might get quite hot though -the higher the Vin the more heat. In fact current x (Vin - 5) = heat power to the regulator.

Given its a high current battery it would be wise precaution to add say a 1A or 500mA fuse on the wire to Vin if possible.You must be very careful never to short out a LiPo pack, they can source huge currents.

Sweet, some great tips! Question - if I short out digital outputs (by accident, of course) would that be equivalent to shorting out the LiPo itself?

No the output pin has more resistance then the battery pack so it would blow something open well before the battery felt the full effects of the short circuit. Fusing your main battery pack is still a good idea, especially for Li-Po cells as they can source a lot of current and overheat and do bad things like catch on fire.

Is it safe to use a 11.1V 1300mAh LiPo Battery designed for RC cars/planes with my new Arduino Nano? I read that the Nano can operate on 6-20V with 7-12V being recommended, so it sounds to me like it would be fine?

Also, I know I plug the positive lead into VIN (pin 30) so do I plug the negative lead into GND?

It's been a while since I've done any electronics tinkering, please excuse my noobiness.

Thanks!

It would be more ideal to use a 2 cell battery (7.4 volts). But, your 3 cell battery would also work. For almost all of my battery-powered projects I use a 2 cell LiPo battery. However, if you plan on running something for a long time that could result in total drainage you should consider monitoring the battery voltage and when tripped it goes into low power mode (watchdog timer) and triggers an alarm. You'll kill your LiPo battery if you drain it to 0 volts, or even 9 volts in your case. Use a resistor-based voltage divider and the internal 1.1 volt reference of the Arduino to measure your battery voltage.